A sampling rate converter is used to change a sampling frequency of a digital signal, and may also be referred to as a re-sampler. A sampling rate converter may take the form of a hardware device and/or software, and may be either an up-sampler or a down-sampler. An up-sampler increases the sampling rate of a digital signal. A down-sampler reduces the sampling rate of the digital signal. A sampling frequency conversion rate is defined to be the ratio of a desired output sampling frequency to a given input sampling frequency. An up-sampling conversion rate is always greater than 1.0, while a down-sampling conversion rate is always less than 1.0.
Aliasing is a phenomenon that usually occurs when converting an analog signal to a digital signal, or vice versa. Aliasing may also occur when converting the sampling frequency of a digital signal. When aliasing occurs, signal energy at one frequency is imaged to other frequencies. For example, suppose a signal has two sinusoidal components at 1 kHz and 7.5 kHz, respectively. If the signal is sampled at 16 kHz, the signal can be reconstructed perfectly. If the signal is down-sampled to 4 kHz from 16 kHz by decimation by 4, the energy at 1 kHz will not change, but the energy at 7.5 kHz will be imaged to 0.5 kHz. The energy at 0.5 kHz is considered aliasing. As another example, if an analog sinusoidal signal at 1 kHz is sampled at 4 kHz, the energy will appear to be at 1 kHz, which is desirable. However, if the signal is up-sampled to 16 kHz by inserting three zeros between adjacent samples, the energy will appear to be at 1 kHz, 3 kHz, 5 kHz and 7 kHz. The energy at 3 kHz, 5 kHz and 7 kHz is an image of the energy at 1 kHz and is considered aliasing. To reduce distortion due to aliasing, sampling rate converters typically include an anti-aliasing filter, which is generally a low pass filter.
Anti-aliasing filters are typically needed in both up-samplers and down-samplers. For example, a conventional up-sampler typically includes an interpolator, which inserts certain number of zeros between adjacent samples and an anti-aliasing filter. Typically, the anti-aliasing filter is a low pass filter with bandwidth π/I, where I is up-sampling factor. As another example, a conventional down-sampler typically includes an anti-aliasing filter and a decimator which periodically picks one sample out of every certain number of samples. Typically, the anti-aliasing filter is a low pass filter with bandwidth π/D, where D is the down-sampling rate.